This study introduces a novel data assimilation framework, Dynamic Compressed Sensing-Dynamic Mode Decomposition(DCS-DMD), for real-time global four-dimensional(4-D) ionospheric electron density imaging and short-term prediction. Unlike traditional methods relying on complex predefined models, the framework employs a Koopman-based algorithm to extract time-varying ionospheric features and integrate them with observational data, enabling simplified and effective ionospheric imaging and prediction. Applied to the May 10–11, 2024 geomagnetic storm, the DCS-DMD model—using Global Navigation Satellite System(GNSS) and Radio Occultation (RO) data at a 5-minute resolution—outperforms existing models in tomographic accuracy. It shows significant improvement in differential slant total electron content(dSTEC) evaluations across reference stations at various latitudes, particularly when combining GNSS and RO data. The model also aligns well with ionosonde measurements, even during geomagnetic storms, detecting a density enhancement at the storm’s onset and a suppression during the recovery phase. Furthermore, the framework demonstrates effective short-term electron density prediction, highlighting its potential for forecasting foF2 in shortwave communication. This model significantly enhances the accuracy of ionospheric imaging and forecasting, providing a streamlined tool for space weather monitoring.

Accurate global-scale ionospheric electron density modeling is crucial for space weather monitoring, exploration, and radio signal applications. This letter presents a novel global-scale ionospheric tomography modeling method, dynamic compressed sensing-principal component analysis (DCS-PCA), building upon the previous region method CS-PCA. The upgraded method operates globally, utilizing dynamic data-driven techniques and undifferenced observation data processing to achieve high-precision quasi-real-time global-scale ionospheric tomography based on global navigation satellite system (GNSS) data. Tomographic models with a 5-min temporal resolution were constructed in this study, utilizing data from various IGS ground stations worldwide and employing the U-DCS-PCA, D-DCS-PCA, and traditional constrained algebraic reconstruction technique (CART). The DCS-PCA model is found to outperform both the CART model and the CODE Global Ionospheric Maps (CODG) model. Specifically, when evaluating differential STEC (dSTEC) errors at independent reference stations across various latitudes, we observed that the error of the DCS-PCA model is not significantly impacted by station sparsity, consistently remaining lower than that of CODG products. In contrast, the error of the CART model increases as the number of stations decreases. Additionally, the U-DCS-PCA model is found to closely align with electron density observations from ionosonde stations. This method is ideal for global 4-D ionospheric monitoring and has potential applications in space weather monitoring, exploration, and radio signal enhancement.

The ionosphere is a vitally dynamic charged particle region in the Earth’s upper atmosphere, playing a crucial role in applications such as radio communication and satellite navigation. The slant total electron contents (STECs) are an important parameter for characterizing wave propagation, representing the integrated electron density along the ray of radio signals passing through the ionosphere. The accurate prediction of STEC is essential for mitigating the ionospheric impact particularly on Global Navigation Satellite Systems (GNSS). In this work, we propose a high-precision STEC prediction model named deep neural operator network (DeepONet)-STEC, which learns nonlinear operators to predict the 4-D temporal-spatial integrated parameter for the specified satellite-ground station ray path globally. As a demonstration, we validate the performance of the model based on GNSS observation data for global and US Continuously Operating Reference Stations (CORS) regimes under ionospheric quiet and storm conditions. The DeepONet-STEC model results show that the three-day 72 h prediction in quiet periods could achieve high accuracy using observation data by the precise point positioning (PPP) with temporal resolution$30~\rm {s}$. Under active solar magnetic storm periods, the DeepONet-STEC also demonstrated its robustness and superiority than traditional deep learning methods. This work presents a neural operator regression architecture for predicting the 4-D spatiotemporal ionospheric state for satellite navigation system performance, which may be further extended for various space applications and beyond.

Ionospheric structure is important for estimating ionospheric delay for user stations in Global Navigation Satellite System (GNSS). However, most existing parameter estimation methods suffer from challenges due to data inaccuracy and unavailability of limited and sparse scattered data at ground reference stations. The high variability of active low latitude or disturbed ionosphere leads to GNSS signal scintillation. It is critical to capture ionospheric random structure and estimate ionospheric parameter using data of disperse receivers to improve accuracy. This paper proposes a unifying method named Ionosphere Kernel Estimation Algorithm (IKEA) to retrieve the information of ionospheric spatial structure. The proposed model utilities the semi-parametric representation theorem to incorporate prior information and constraints. The multiple kernel technique is adopted firstly to include physical correlations. Additionally, a learning approach is deployed to determine model parameters. The IKEA model has been verified based on simulated and experimental data at active low latitudes from a network of ground GNSS reference stations from all visible GPS and GALILEO satellites. The IKEA model reduces approximately 19.5% and 24.2% of differential Slant Total Electron Content (dSTEC) in the root mean square error with respect to Inverse Distance Weighting (IDW) and the Kriging model during high ionospheric activities. The IKEA architecture has been demonstrated effective to make robust ionospheric estimation, which may be further extended for various GNSS applications and beyond.

3-D computerized ionospheric tomography (CIT) is an ill-posed problem due to the insufficient amount of observations, it remains challenging for practical applications. In this article, we proposed an ionospheric tomography method that combined data-driven methods with compressed sensing (CS) to deal with the ill-posed problem. First, slant total electron content (STEC) data were extracted by undifferenced and uncombined precise point positioning (UCPPP) with known fixed station coordinates. Second, data-driven methods were adopted to construct the projection matrix from the ionospheric model. Third, compressed sensing was used to derive the sparse solution based on$L_{1}$norm. The ionospheric tomography can be achieved well by using observations during the shorter time interval and in a sparse receiver distribution based on the property of compressed sensing. Results of experiment based on real Global Positioning System (GPS) observation data verified the effectiveness of the proposed methods. By comparing with the colocated ionosonde, it is found that the CS methods are more consistent with the actual ionospheric fluctuation than the modified constrained algebraic reconstruction technique (CART). In terms of the differential STEC (dSTEC) analysis, the error of the tomography model by Compressed Sensing-Principal Component Analysis (CS-PCA) is less than 0.2 TEC unit (TECU), and the time resolution is 5 min. The UCPPP with constraint by CS-PCA shows the best performance of 12.2%, 40.9% and 0.31% improvement in positioning accuracy, convergence time, and fixed rate over the UCPPP with constraint by modified CART. The proposed data-driven methods may be important for high-resolution 4-D ionospheric tomography in the future.

TwinSAR-L (Terrain Wide-swath Interferometric L-band SAR mission) is an innovative space-borne bistatic SAR mission for global dynamics, which will be launched in 2020. This paper investigates ionospheric effects on phase and Faraday rotation of interferometry for TwinSAR-L systems. This ionospheric offset arises from different incident angles along each path in inhomogeneous ionosphere. Plus, the inhomogeneity of ionospheric TEC will cause different range delay and defocusing due to dispersion and azimuth shift. The analysis in this paper will be important for TwinSAR-L mission and potential Tandem-L mission in the future.